7. Consider the function f(x)==-²₂.a. By graphing the function, explain why f is one-to-one.b. Find a formula for the inverse function of f (call this function f-¹).c. What is the value of f-¹(f (8))?d. What is the value of f(f¹(49))?8. At CheapCo Convenience Stores, employees receive an increase in their hourly wage each year.A certain employee's hourly wage in dollars per hour, t years after she starts working forCheapCo, is given by the formula w(t) = 9.50 +0.30t.a. What is w(10)? What does this value tell us about the employee's hourly wage?b. What is w¹(14)? What does this value tell us about the employee's hourly wage?In real life, why might somebody be interested in finding and understanding the inversefunction w ¹7c.

Answered: 7. Consider the function f(x)=₂ a. By…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

7. Consider the function f(x)==-²₂.
a. By graphing the function, explain why f is one-to-one.
b. Find a formula for the inverse function of f (call this function f-¹).
c. What is the value of f-¹(f (8))?
d. What is the value of f(f¹(49))?
8. At CheapCo Convenience Stores, employees receive an increase in their hourly wage each year.
A certain employee's hourly wage in dollars per hour, t years after she starts working for
CheapCo, is given by the formula w(t) = 9.50 +0.30t.
a. What is w(10)? What does this value tell us about the employee's hourly wage?
b. What is w¹(14)? What does this value tell us about the employee's hourly wage?
In real life, why might somebody be interested in finding and understanding the inverse
function w ¹7
c.

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Introduction:

A function that will reverse into another function is thought of as a mathematical function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as " $f^{- 1} o r F^{- 1}$ ".